Finite Group Databasebeta

← #13024825

Subgroups — #13024825

Order 1280.

280 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614743C211yesmaximal, characteristic
2#10604155C212yesmaximal, complemented
3#10598736C212yesmaximal, complemented
4#10598735C212yesmaximal, complemented
5C2×C5×#125C411yescharacteristic
6#65811C411yescharacteristic
7#65358C411yescharacteristic
8#65358C2211yescharacteristic
9#65357—22no—
10#65356C411yescharacteristic
11#65356C2211yescharacteristic
12#65255—22no—
13C4×#681C2211yescharacteristic
14#64912—22no—
15#64861—22no—
16#64860C2214yes—
17#11917—51nomaximal, Sylow
18C2×#709—21no—
19C5×#125—21no—
20C5×#125—41no—
21C5×#125C2×C411yescharacteristic
22C5×#125C2×C411yescharacteristic
23C2×C5×C4⋊C4—21no—
24C2×C5×C4⋊C4—41no—
25C2×C42×C5C2×C411yescharacteristic
26#4076—41no—
27C2×#681D412yes—
28#4021—21no—
29#4020C2×C411yescharacteristic
30C4×D20—41no—
31#4015C2×C411yescharacteristic
32#3998—24no—
33#3942—22no—
34#3942—22no—
35#3941—22no—
36#3941—22no—
37#3935C2×C411yescharacteristic
38#3935C2311yescharacteristic
39C4×#168D412yes—
40#3142—51no—
41#2165—52no—
42#1356—52no—
43#1355—52no—
44C22×C4×C5—21no—
45C22×C4×C5—41no—
46C22×C4×C5C22⋊C411yescharacteristic
47C2×C22⋊D5—41no—
48#709—44no—
49C2×D20—21no—
50C2×D20—41no—
51C2×C4×D5—41no—
52C2×Dic10—21no—
53C5×C4⋊C4—21no—
54C5×C4⋊C4—21no—
55C5×C4⋊C4—41no—
56C5×C4⋊C4—41no—
57C5×C4⋊C4—42no—
58C5×C4⋊C4—41no—
59C42×C5—21no—
60C42×C5C22⋊C411yescharacteristic
61C42×C5C22×C411yescharacteristic
62#685—42no—
63C4⋊Dic5—41no—
64#681—42no—
65C2×#168C22⋊C412yes—
66C2×#168C2×D412yes—
67#674—44no—
68#532—51no—
69C2×#125AGL(1,𝔽5)11yescharacteristic
70#491—51no—
71#491—51no—
72#490—51no—
73#490—51no—
74#488—102no—
75#417—102no—
76C4×M16—51no—
77#364—102no—
78#349—102no—
79#347—54no—
80C23×C5#10011yescharacteristic
81C22×D5—41no—
82C2×C4×C5—22no—
83C2×C4×C5—21no—
84C2×C4×C5—21no—
85C2×C4×C5—41no—
86C2×C4×C5—41no—
87C2×C4×C5—81no—
88C2×C4×C5—82no—
89C2×C4×C5#10011yescharacteristic
90C2×C4×C5C2×C22⋊C411yescharacteristic
91C22⋊D5—82no—
92C2×Dic5—41no—
93D20—42no—
94D20—82no—
95C4×D5—82no—
96Dic10—42no—
97#168—22no—
98#168—22no—
99C2×#41—101no—
100C2×M16—52no—
101C4⋊Q8—51no—
102#127—51no—
103#125—21no—
104#125—41no—
105#125C2×AGL(1,𝔽5)11yescharacteristic
106#125C2×AGL(1,𝔽5)11yescharacteristic
107#124—101no—
108#121—201no—
109C4×D4—201no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—41no—
112C2×C42C2×AGL(1,𝔽5)11yescharacteristic
113M32—104no—
114#103—102no—
115#103—102no—
116#102—102no—
117#102—102no—
118#97—51no—
119#97—51no—
120C4×C8—52no—
121C22×C5—21no—
122C22×C5—41no—
123C22×C5C2×#10011yescharacteristic
124C2×D5—82no—
125C2×D5—81no—
126C4×C5—21no—
127C4×C5—41no—
128C4×C5—41no—
129C4×C5—81no—
130C4×C5—81no—
131C4×C5#42112yes—
132Dic5—81no—
133#41—204no—
134C2×Q8—101no—
135C2×D4—101no—
136C2×D4—201no—
137C2×D4—201no—
138C22×C4—21no—
139C22×C4—41no—
140C22×C4—201no—
141C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
142M16—202no—
143C2×C8—52no—
144C2×C8—52no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—42no—
150C4⋊C4—41no—
151C4⋊C4—201no—
152C22⋊C4—202no—
153C42—21no—
154C42C22⋊AGL(1,𝔽5)11yescharacteristic
155C42C22×AGL(1,𝔽5)11yescharacteristic
156C16—204no—
157C2×C5—21no—
158C2×C5—41no—
159C2×C5#153311yescharacteristic
160D5—161no—
161C23—201no—
162C23#401311yescharacteristic
163Q8—202no—
164D4—202no—
165D4—402no—
166D4—402no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—82no—
174C2×C4—201no—
175C2×C4—402no—
176C2×C4#401311yescharacteristic
177C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
178C8—102no—
179C8—102no—
180C5#1191711yescharacteristic, complemented, Sylow
181C22—21no—
182C22—41no—
183C22—402no—
184C22—401no—
185C22C2×#401311yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—81no—
190C4—81no—
191C4—401no—
192C4#6578412yes—
193C2—21no—
194C2—41no—
195C2—801no—
196C2#1060496111yescharacteristic
subgroupG/H
centerC2#10604961
commutatorC42×C5C22×C4
FrattiniC42C22×AGL(1,𝔽5)
FittingC2×C5×#125C4
socleC2×C5#1533
prime radical#65811C4
cosocle#3935C23
hypercenterC2×#125AGL(1,𝔽5)
hypocenterC5#11917
LCSG ▷ C42×C5 ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×#125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10604155C2semidirect
3. #10598736C2semidirect
4. #10598735C2semidirect
180. C5#11917semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106147432
#106041552
#105987362
#105987352
#119175